📊Sample Size Calculator
Use 50% if unknown
Sample size is the number of observations needed in a study to achieve a specified margin of error and confidence level. Larger samples give more precise estimates but cost more to collect. The required n depends on confidence level, expected proportion, and acceptable error.
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Tip: Always calculate sample size before collecting data. Stopping early when results look significant ("peeking") inflates your Type I error rate dramatically.
- 1For proportions: n = z² × p(1-p) / E²
- 2z = 1.96 for 95% confidence · z = 2.576 for 99% confidence
- 3p = expected proportion (use 0.5 if unknown — gives maximum n)
- 4E = desired margin of error as a decimal (e.g. 0.05 for ±5%)
95% confidence · ±5% margin · p=0.5=n = 3841.96²×0.5×0.5/0.05²=384.16 → round up to 384
99% confidence · ±3% margin · p=0.5=n = 1,844Tighter margin + higher confidence = far more observations
| Population | Required sample |
|---|---|
| 500 | 217 |
| 1,000 | 278 |
| 10,000 | 370 |
| 100,000 | 383 |
| Infinite | 384 |
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Fun Fact
For proportions, a sample of 384 gives ±5% margin of error regardless of whether the population is 1,000 or 1 billion — which is why national polls of ~1,000 people are statistically valid.
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